Timelapse video of the Higgs Boson Discovery plot evolution

July 8, 2012

Tevatron squeeze 2.9 sigma Higgs Signal

July 2, 2012

The CDF and D0 experiments have presented new results today that provide a slight improvement on their previous results shown at Moriond in March. The significance has risen to 2.9 sigma coming mostly from the dominant decay channel to bottom quarks. No new data has been added since the Tevatron closed down last year but analysis has continued to look for further decay channels in the data and improve the analysis of the ones already used. In particular they have improved the analysis of bb decays where the Higgs boson is produced in conjunction with a W or Z vector boson.

This is the current state of the combination. They have said that they are not finished yet with the possible improvement by 10% in some areas so we should see further updates. All eyes will now turn to CERN where a much more dramatic update is expected in Wednesday, but the Tevatron results remain important because the LHC is not so sensitive to the bb channel which is important for showing that the Higgs couples correctly to fermions.

Interest in the Higgs news is already rocketing with #Higgs and “God Particle” both trending on Twitter while over 1250 viewers are watching the live stream from the Tevatron.

Update: Here is the latest version of the unofficial global Higgs combination with the new results from D0 included. The significance at 125.5 GeV has crept up to 4.4 sigma.

Moriond 2012 Higgs Summary

March 8, 2012

… or perhaps I should be calling it the “Brout-Englert-Higgs” Summary or even the “SM scalar boson” Summary. These were the titles diplomatically chosen by the speakers in the presence of François Englert who gave the opening talk for the session, but the particle is still symbolised by just the letter H.

The Moriond meeting has seen another small step forward in the search for the missing boson with new data coming from the Tevatron and LHC experiments. Now that all the plots are available online it’s a good time to pick out a few highlights and see what they are telling us.


I showed the Tevatron combined plot yesterday with its comforting 2.2 sigma excess from 115 GeV to 135 GeV. Here are the individual plots from CDF and D0

These are comfortably consistent with a Higgs between 115 GeV and 135 GeV and could accommodate a wider range. 2.2 Sigma is not a high significance level but in conjunction with results from the LHC it is a nice independent confirmation of what they are seeing.

There is one further point to make about this result that is very important and so far overlooked. The Tevatron is getting its signal from the bb channel. Below is my unofficial combination for the decay channel to two bottom quarks alone. CDF and D0 were able to get a lot more information out of this channel than previously by improving their algorithm for identifying the hadronic jets coming from these decay products. It is not an easy business and results in a widely spread excess as seen here.

What makes this especially interesting is that this shows the Higgs decaying to two spin-half fermions. The LHC has so far only had tentative signals in the diphton, WW and ZZ channels which are all spin one products. Spin in conserved in the decay process so a scalar boson with its spin of zero can decay into two particles of equal spin orientated in opposite polarisations so that the total spin cancels out. the experiments cannot measure the orientation of the spin so if they see two photons (or W or Z bosons) they can only say that the spin of the original particle was zero or two. Someone wanting to be argumentative could say that the particle being discovered is a graviton like spin two boson. However, if we take the Tevatron excess to be a signal of the same particle then we also know it can decay into two spin half fermions. That would indicate a particle of spin zero or spin one. Putting the two results together we know that it can only be spin zero which is a nice confirmation for the theory of the Higgs mechanism. It will be a long time before the LHC can get a similar result from the bb channel so this observation makes the Tevatron result much more than just a small confirmation.


Following the Tevatron presentations ATLAS was next up to present. After the major update in December they still had a number of channels to update to use the full 5/fb of data collected in 2011. This included H -> ττ, H -> bb, H-> WW -> lνlν,  WW -> lνqq, ZZ -> llqq and ZZ -> llνν. Of these only the first three are relevant to the low mass scale of interest.  The  H -> ττ, H -> bb do not have much sensitivity yet so no excess was expected there. This leaves only the  H-> WW -> lνlν channel to be of any real interest. Here is what is looks like at low mass.

There is not much excess in this plot so the effect of updating it is to drop the combined excess for ATLAS at 125 GeV from 3.5 sigma previously to 2,5 sigma now. Here is what it looks like. Some media outlets such as New Scientist are reporting this as a “fading” signal. There are two points that need to be made to mitigate here.

Firstly, the WW channel has very low mass resolution made worse in the latter part of the run by increasing event pile-up. We should only expect a broad excess in this plot rather than a nice peak indicating the mass of the Higgs boson. Let me quote again something I said about this back in September last year.

Our expectation is that as more data comes in a sharp peak (or two) will emerge somewhere in the low mass region to reveal where the Higgs is. However, the plot is dominated by the WW channel over most of this range and the WW channel has low resolution. This is because it uses missing energy observations to construct the underlying mass of the events. The W’s decay into neutrinos which can never be detected directly. The result is that the Higgs appears as a broad excess in the WW channel and you can’t locate it well. The WW channel is great for excluding large ranges of the mass spectrum, but it is not good for pinpointing a low mass Higgs that has a narrow width.

Furthermore, the situation will not improve as more data is added. The WW channel will always remain low resolution and it will always dominate the combination plot. Sadly the Tevatron data has the same problem. It is dominated by WW and bb channels with neutrinos in each case. In fact the detectors themselves have poorer resolution and even the digamma and ZZ channels are only ever plotted at 5 GeV intervals for the Tevatron. So what should we do? if some data could be making the plot worse the best thing is to remove it and see what we get.”

In other words the WW channel does not help the combination and is best left out, but they would not want to be accused of cherry picking so it stays. They have however given us this complicated version of the plot that shows separates the low resolution  and high-resolution channels for just this reason.

My second point is that the current excess in the diphoton channel is actually a little larger than the standard model predicts. This can be accounted for as a statistical fluctuation, but likewise the deficit in the WW channel is consistent with a normal fluctuation in the opposite direction. In fact the combination with its now weakened excess is now closer to what the standard model predicts and we should be happier!


CMS had already updated all their channels with all the available data last month so we did not expect much new from them. Nevertheless they have carried out an MVA analysis of the important diphoton channel to get more out of it. The result is this new plot

They even managed to find some completely new channels such as WH-> WWW. The result is yet another new CMS combination.

All this means I now owe you a new combination for ATLAS+ CMS and here it is

This now excludes the full range of masses except a narrow window from 122 GeV to 128 GeV. This is a remarkable achievement when you consider that at Moriond 2011 a year ago the LHC could tell us essentially nothing about the Higgs boson.

The best evidence we now have for the existence of the Higgs boson still comes from the diphoton channel. Combining all four experiments it now looks like this

Some people have said that it is really only this channel that supports the case for the Higgs boson at 125 GeV but that is no longer the case. Here is what you get if you combine just the bb and ZZ channels globally

There is still a long way to go but I certainly think the case for a standard model Higgs boson at around 125 GeV now looks good. Even the outside possibility for something more at a lower mass below 120GeV has now faded with the LHC combination excluding that region. It remains hard to get a combination that combines to give an overall significance above the crucial 4 sigma level and we may have to wait some time for that.

Finally I leave you with this impressive plot of the combined Higgs signal from ATLAS and CMS.

Tevatron posts excess with final Higgs results

March 7, 2012

Today is another big day for the Higgs boson and this time it is the turn of Fermilab to give us some new information. The venue for the latest offerings is the conference in Moriond. The talks are still ongoing but the main plot has already been shown. (see QDS)

Later I will give a new combination with the LHC results which may also be updated today, but for now here is a useful variation on the plot showing it as a Signal curve. In this plot the zero line represents no Higgs boson while the line at one is expected for the standard model Higgs boson. What we see is a signal perfectly consistent with a boson in the mass region of about 115 GeV to 140 GeV. The mass resolution is not as good as the LHC results and the significance of the excess is less but consistency with the other results is what we were hoping for, so well done to CDF and D0 for this nice final Higgs result from them.

Update: Here is the combination of the new Tevatron data with the latest ATLAS and CMS. On the left is just ATLAS+CMS on their own, and on the right the Tevatron is included. (Remember these are just my unofficial approximate combinations) The result is a small improvement in the overall level of the peak excess.

Mini Higgs Update

March 2, 2012

Today at La Thuile physicists from the Tevatron and LHC have been giving out a few teasers in preperation for the next Higgs updates expected at Moriond.

Dzero have released a diphoton plot as their first Higgs channel result using the full Tevatron dataset of 9.7/fb (Satish Desai Desai)

This is a companion to the equivalent plot from CDF published a month ago. At the LHC this is the most exciting channel but at the Tevatron it does not reach the sensitivity required to tell us anything about a standard model Higgs.

Slightly more interesting is this WW channel plot from CDF which improves on previous limits by about 10% (Richard StDenis). This is close to the sensitivity where some excess could have emerged but nothing is apparent.

The real interest for the Tevatron is the Higgs decay to two bottom quarks (bb channel) . For that and the combinations we are told to wait until next week which probably means Moriond.

ATLAS and CMS have not provided any new plots yet but ATLAS have reminded us that they still have to update WW, bb and ττ at 5/fb and we are also told to expect news at Moriond from them.

The ATLAS+CMS combinations previously expected for Moriond have apparently been abandoned. With the peak excesses from the two experiments in slightly different places the benefit of doing the combination may not justify the resources needed to produce it. Instead they look set to aim for independent discoveries from both ATLAS and CMS by the end of the year. This will not be an easy task as this plot at the bottom of the ATLAS talk shows (Junichi Tanaka) The 8 TeV energy improves the cross section by 30% and 3 sigma sensitivity is within easy reach with 2012 data, perhaps even in time for ICHEP, but 5 sigma discovery quality results require the full years run and some good luck. A run extension and a combination with 2011 data may be needed to polish it off. The same goes for CMS of course, and there is always the possibility that they will end the year with one team having better luck than the other.

In any case the arrow on this plot shows that they already know where the Higgs is :)

CMS also presented today (Josh Bendavid) but they have already given us everything they have for Higgs in 2011 data.

Shutdown approaches for the Tevatron

September 28, 2011

They say that all good things must end and it is certainly true for the Tevatron. The US hadron collider based at Fermilab will finally shutdown in just two days time. The last moments when the switch is thrown to kick the store of protons and anti-protons into the graphite dump blocks will be webcast live from the control rooms at 2 p.m. CDT on the 30th of September. There will be celebrations but they are likely to be somewhat muted. The operators would have liked to continue for the chance of finding the Higgs boson before their European rivals at CERN but congress refused the funding.

The Tevatron’s greatest discovery was the Top quark which it found in 1995. In 2002 the new higher luminosity run II began. Between then and the final day the two detectors CDF and D0 will have recorded about 10.7/fb worth of collision events. Run II has had many smaller successes including the exclusion of the Higgs boson over a range of masses but it has missed out on the opportunity to take the prize for its discovery. That glory will now almost certainly go to the LHC. When Run II began the LHC had just been approved and was expected to start running in 2005. Project delays and funding reviews pushed that back to 2007. Then further delays due to accidents that damaged the magnets meant that the final startup date was the end of 2009 with the first serious data being recorded in 2010. It is tempting to wonder if things would have been different if it had been expected earlier that the LHC would start operating so late.

The recent decision to end the Tevatron was I think the right one. It had become clear that the LHC results would overshadow anything that it could now produce. Fermilab has remained optimistic that their final total will help find the Higgs. If you add the Tevatron data to the LHC Higgs plots it makes a difference at the low mass end where we now think the Higgs is hiding. In this plot the black line is the unofficial combination for the latest LHC data while the red line shows a fuller combination with CDF and D0 included too.

But that is not the whole story. While the LHC is starting to see bumps that might be the first hints of where the Higgs could lie, the Tevatron just sees a broad and statistically weak excess. The difference may be that the detectors at the LHC have much better energy resolution. They are next generation gadgets in a world where technology is moving very fast. At low mass the Higgs resonance is narrow and they will need good energy resolution to see it well.

I am not sufficiently well versed in the lore of detectors to know if the Tevatron could have beaten the LHC to the Higgs discovery if they had put more into the collider before the start of Run II. I know that some opportunities to upgrade the detectors were passed over. Perhaps that would have been sufficient to see the signal the Higgs produces. With the benefit of hindsight we can see that things might have been done differently if they had known of the delays that would befall the LHC.

The race between the LHC and the Tevatron has been a classic hare against tortoise story and as in the original Greek drama the hare took its time to get going. Two years ago when the LHC was just starting up, the Tevatron had already excluded the Higgs at 170 GeV. If it had been sitting at that mass there is little doubt that the tortoise would have claimed the prize. In this real life version of tale however,  the distance to go was a little longer and now the hare is coming through to take the finish line.

This will certainly not be the end of the story for the accelerator complex at Fermilab. Stopping the Tevatron gives a chance for neutrino experiments to take over the injectors. Two new neutrino experiments will be added to help in a field of research where there are many mysteries to be resolved. Another line of development known as project X will explore the intensity frontier with muon beams and perhaps eventually an ambitious muon collider will be funded. The future for collider physics in the US now depends on the choices that the government has to take.

Higgs Days at Santander

September 18, 2011

Santander is a Spanish port on the Bay of Biscay coast that next week will host its fourth annual workshop on the Higgs Boson. This meeting will be very different in character from the huge summer conferences where exciting new results on searches for the Higgs boson were recently presented to thousands of physicists. The Santander meeting involves just 30 participants with a mix of theorists and experimenters involved in the analysis of data from Fermilab and CERN. Half their time will be spent presenting slides and the other half will be discussions covering searches for standard model Higgs and other models including the charged Higgs sector of SUSY. They will talk about the procedures for combining Higgs searches across experiments and implications of any findings. The aim is to promote a dialog between theorists and experimenters about what data needs to be shared and how.

Santander beaches, photo by yeyo

There is no indication that the discussions will be webcast or recorded for public viewing and it is not sure that all the slides will appear online so as outsiders the rest of us may have very little indication of what they decide. It is unlikely that new data will be made public but there is some chance that we may finally get to see a combination of ATLAS and CMS search data. Originally we were promised a combination of the searches shown at EPS in July using the first 1/fb of data from the LHC. Instead we got a new helping of plots from the individual experiments using 1.6/fb in the most important channels and even 2.3/fb for the ZZ channel in ATLAS. These were shown at the Lepton-photon conference in August. Theorists would now very much like to see the combinations of these data sets and it is not clear why they have been held back.

One question has become very topical and has already surfaced at some of the larger Higgs workshops: Is it right to do quick approximate combinations of Higgs search data or do we need to wait for the lengthy process of producing the official combinations? This summer I have become quite notorious for doing these quick combinations and showing them on viXra log. These have variously been described by experts as “nonsense” (Bill Murray) “garbage” (John Ellis) and “wrong” (Eilam Gross), but just how bad are they? Here is a plot of my handcrafted combination of the D0 and CDF exclusion plots compared with the official combo. The thick black line is my version of the observed exclusion limit that can be compared with the dotted line of the official result, while the solid blue line is may calculated expected limit to be compared with the official dashed line. You need to click on the image for a better view.

My result is not perfect but I hope you will agree that it provides similar information and you would not be misled into drawing any wrong conclusions from it that were not in the official plot. Any discrepancy is certainly much smaller than the statistical variations indicated by the green and yellow bands for one and two sigma variations.

A more ambitious project is to combine exclusion plots for individual channels to reproduce the official results for each experiments. Here is my best attempt for the latest ATLAS results where I have combined all eight channels for primary decay products of the Higgs boson.

The result here is not as good and could only serve as a rough estimation of the proper combination. Why is that? There are several sources of error involved. Firstly the data for the individual channels had to be digitised from the plots. This was not the case for the previous Tevatron combination above where they published the plots in tabular form. ATLAS and CMS have only published such numerical data for a few channels and in some cases the quality of the plots shown is extremely poor. For example this is the best plot that ATLAS has shown for the important H → ZZ → 4l channel

As you can see it is very hard to follow the lines on this plot, especially the dashed expected limit line. I don’t want to be over-critical but seriously guys, can’t you do better than this?

Another source of error comes from neglect of correlations between the individual plots where background estimates may have the same or related systematic errors. The Higgs combination group at CERN play on this as one of the reasons why these quick combinations can’t be right, but I doubt that these effects are significant at all. If they were I would not be getting such good results for the Tevatron combination.

In fact the main source of error is in approximations used in my combination algorithm. It assumes that each statistical distribution of the underlying signals can be modeled by a flat normal distribution with a mean \mu_i and standard deviation \sigma_i. Combining normal distributions is standard stuff in particle physics the combined mean \mu and standard deviation \sigma are given by these formula

\frac{1}{\sigma^2} = \sum_i{\frac{1}{\sigma_i^2}}

\frac{\mu}{\sigma^2} = \sum_i{\frac{\mu_i}{\sigma_i^2}}

For example, if one experiment tells me that the mass of the proton is 938.41 ± 0.21 GeV and another tells me it is 938.22 ± 0.09 GeV and I know that the errors and independent, then I can combine with the above formula to get a value of 938.25 ± 0.08 GeV. The Particle Data Group does this kind of thing all the time.

A plot of the signal for the Higgs boson given by the ATLAS results would look like this,

The black line (value of \mu) is the observed combined signal for the Higgs boson normalised to a scale where no Higgs boson is zero and a standard model Higgs boson gives one. The blue and cyan bands show the one and two sigma statistical uncertainty (\mu \pm\sigma and \mu \pm 2\sigma). Don’t think about where the Higgs boson is for now. Just look at the upper two sigma level curve and compare it with the ATLAS Higgs exclusion plot above (i.e the dotted line, click to enlarge for a better view). These are of course the same lines because the 95% level exclusion is given when the 2 sigma error is below the signal for SM Higgs. The expected line on the exclusion plot is just where the observed line would be if the signal were evrywhere zero, i.e it is a plot of 2\sigma. In summary, the observed limit for CL_s in the exclusion plot is just \mu + 2\sigma and the expected limit is just 2\sigma. We can derive one plot from the other using this simple transformation.

From this it should be clear how to combine the exclusion plots. We first transform them all to signal plots, then they can be combined as if they are normal distributions. Finally the combined signal plot can be transformed back to give the combined exclusion plot. This is what I did for the viXra combinations above.

Ignoring the digitisation errors and the unknown correlations, the largest source of error is the assumption that the distribution is normal. In reality a log normal distribution or a Poisson distribution would be better, but these require more information. Fortunately the central limit theorem tells us that anything will approximate a normal distribution when high enough statistics are available so the combination method gets better as more events accumulate. That is why the viXra combination of the exclusion plots for each experiment is more successful than for the combination of individual channels. The number of events seen in some of these channels is very low and the flat normal distribution is not a great approximation to use. As more data is collected the result will get better. Of course we cannot expect a reliable signal to emerge from individual channels until the statistics are good, so it could be argued that the approximation is covered by the statistical fluctuations anyway.

I don’t know if a full LHC combination will emerge next week at the Santander workshop but in case it does, here is my best prediction from the most recent data for comparison with anything they might show.

Some people say that there is no point producing these plots because the official versions will be ready soon enough, but they are missing the point. The LHC will produce vasts amounts of data over its lifespan and these Higgs plots are just the beginning. The experimenters are pretty good at doing the statistics and comparing with some basic models provided by the theorists, but this is just a tiny part of what theorists want to do. The LHC demands a much more sophisticated relationship between experimenter and theorists than any previous experiment and it will be necessary to provide data in numerical forms that the theorists can use to investigate a much wider range of possible models.

As a crude example of what I mean, just look at the plot above. It provides conflicting evidence for a Higgs boson signal. At 140 GeV there is an interesting excess but it is below the exclusion limit line. Is this a hint of a Higgs signal or not? To answer this I might look at different channels combined over the experiments. Here is the ZZ channel combined over ATLAS and CMS.

The Higgs hint at 140 GeV is now nice and clear, though not significant enough yet for a reliable conclusion. Here is the diphoton channel combination.

Again the 140 GeV signal is looking good. What about the WW channel?

Here is where the problem lies. The WW channel has a broad excess from 120 GeV to 170 GeV at 2 sigma significance, but it is excluded from about 150 GeV . In fact the energy resolution in the WW channel is not very good because it relies on missing energy calculations to reconstruct the neutrino component of the mass estimation. Perhaps it would be better to combine just the diphoton and ZZ channels that have better resolution. I can show the result in the form of a signal plot.

It’s still inconclusive, but at least it is not contradictory.

This is just as example of why it will be useful for theorists to be able to explore the data themselves. The signal for the Higgs will eventually be studied in detail by the experiments, but what about other models? There is a limit to how many plots the experiments can show. To really explore the data that the LHC will produce theorists will need to be able to plug data into their own programs and compare it with their own models. The precise combinations produced by the Higgs combination groups take hundreds of thousands of CPU hours to build and are fraught with convergence issues. My combinations are done in milliseconds and gives a result that is just as useful.

There is no reason why the experiments can’t provide cross-section data in numerical form for a wide range of channels with better approximations than flat normal distributions if necessary. This would allow accurate combinations to be generated for an infinite range of models with varying particle spectra and branching ratios. It will be essential that any physicist has the possibility to do this. I hope that this is what the theorists will be telling the experiments at Santander next week and that the experiments will be listening.

Update 26 Sept 2011: I found a better version of the ATLAS ZZ -> 4l plot that I was moaning about. It has not appeared in the conference notes for some reason but it is same data from LP11 so I think it must be OK to show.

The latest expectation from the combination group is that a Lepton-Photon based combo will be ready for  Hadron Collider Physics 2011 which is in Paris starting 14th November.

Update 1-Oct-2011: Most of the slides from the Santander meeting have now been uploaded

Higgs Signal Plots

August 23, 2011

It is traditional to present the results of searches such as Higgs hunting as Brazil plots that show us where a signal can be excluded at 95% confidence, but when the data starts to show a positive signal it is better to show signal plots like the one below. This is just the observed confidence level limit minus the expected with the error bands for one and two sigma statistical variation shown around the signal level line.

In this plot an absence of a Higgs boson is indicated by the black line being at the red zero line, but the presence of a standard model Higgs is indicated by meeting the green line at one.

Here I am using the latest CMS and ATLAS data shown at Lepton-Photon 2011 as well as the Tevatron combination shown at EPS 2011

This gives a much clearer picture of what is going on. Above 155 GeV the signal is nicely consistent with no Higgs. Below 135 GeV the signal is right in the middle but the error bands are large and easily allow for either a Higgs or no Higgs.

The middle region is more interesting. From about 135 GeV to 150 GeV it disfavours both a signal and no signal of a standard model Higgs. It is tempting to say that this rules out standard model physics in this region but I think it is too soon to draw such a conclusion. It may be that there is a SM Higgs boson at say 140 GeV but the resolution is not sufficiently good to get a clean signal there, or more data may see the line fluctuate down to the no signal level.

It is important to remember that we are still at the stage where just a few signal events have a big effect on the curve. More detail will emerge with more data. Furthermore, the plot above is only an approximation that does not properly take into account all uncertainties and correlations.

The LHC is now entering a Machine Development and Technical Stop phase for the next two weeks with 2.5/fb recorded in each of ATLAS and CMS. There are no big conferences on the horizon but both experiments have CERN seminars scheduled for the middle of September. With luck they might update all the channels and give us another update soon. Hopefully they will also do some official combos for both exclusion and signal plots.

In case you were wondering what it would have looked like with the EPS data, here it is.

Better Higgs Combinations

August 6, 2011

During the recent EPS conference when some new Higgs Exclusion plots were unveiled I has a stab at putting together some combinations of the plots using some basic formulas. Despite the broad caveats I gave them the plots got a surprising amount of attention. At a plenary session during EPS Bill Murray referred to my plots as “nonsense based on absolutely nothing” (which is not too far from the truth). Then at the Higgs Hunting workshop that followed EPS, John Ellis showed my “bloggers conbinations” saying that they were garbage but in the absence of anything better he would use them anyway. I hope this all added to everyone’s amusement and excitement as all the great new results were shown and discussed.

The formulas I used in those combinations were just quick guesses but they worked quite well for the Tevatron combination of CDF and Dzero Higgs results. In two or three weeks the LHC will reveal their combination for ATLAS and CMS at the Lepton-Photon conference in Mumbai so we will see how well my combination for that worked too.

Now that there has been a little more time to think about it I have looked at the basic statistic theory behind the plots to see why my formulas worked (so far). As a result I have come up with some improvements so I want to show some new plots that I think will be more accurate.  There will be many more plots to combine in the near future as the LHC and Tevatron continue to churn out more data, so if they do work even approximately they may have some real use.

First some theory. Imagine you are looking for a signal of new physics in some decay channel. The standard model (without Higgs) will predict a certain background cross-section b in a given mass bin. The new process (such as a Higgs decay) will add a signal cross section s to give a total cross-section b+s . After gathering lots of integrated luminosity L you may see N events with the required signal so you calculate the observed cross-section x = \frac{N}{L} . Now you are interested in whether x corresponds to the background b  or the background plus signal b+s . In practice you can’t be sure so you have to look at the uncertainty.

To make things even simpler I am going to assume that the signal is smaller than the background but there are plenty of events N . For a Higgs search this is a better approximation for low mass than for bigger mass but there are lots of other things we are going to ignore so why not start here?

Our estimate of the cross section x has an uncertainty which we can write as \sigma = \pm \frac{x}{\sqrt{N}} . One thing we can say is that with 95% confidence the cross section is less than a limit x + 2 \sigma . We calculate the limit minus the background over the expected signal

CL_s = \frac{x -b +2 \sigma}{s}

If this is less than one it means that the cross-section is less than the signal required for the Higgs boson with 95% confidence. This is roughly what the experiments plot against the Higgs mass. They also look at background uncertainty, trial error and combine different channels in a non-trivial way, but let’s ignore those things and see what happens. The expected value if there is no signal is just what we would get for CL_s if x = b . This is also added to the plot as a function of mass with the familiar green and yellow uncertainty bands.

Now imagine that there are two experiments measuring the same quantity. They have different amounts of luminosity recorded and may be working at different energies and they will surely see different number of events. For now let’s pretend the background and signal are the same for each. This would be roughly true for two experiments at the same collider, but since the actual values of these numbers will not enter into the final formula we can try and use it even for different colliders.

For experiment 1 the observed value of CL_s is

c_1 = \frac{x_1 (1 + \frac{2}{\sqrt{N_1}}) - b}{s}

and for the expected value it is

e_1 = \frac{2 b}{ s \sqrt{ b L_1} }

Similarly for experiment 2 with observed and expected CL_s , c_2 and e_2. If we combine the two sets of events we will have N = N_1 + N_2 events in total, and total Luminosity L = L_1 + L_2 . This combination of luminosities can be substituted into the formula for excpected CL_s to derive the following combination law

e = \frac{1}{\sqrt{\frac{1}{e_1^2 } + \frac{1}{e_2^2 }}}

This is exactly the formula I used before, so far so good. However I used the same formula to combine the observed $CL_s $, this was not quite correct. The excess \Delta = c - e is given by

s \Delta = (x - b) (1 + \frac{2}{\sqrt{N}} )

Using the large N approximation this reduces s \Delta = x - b . If you dont like this approximation and you know the signal to background ratio you can improve it. I found that this does not make much difference in practice.

The observed cross-sections combine with weights given by the luminosities

x L = x_1 L_1 + x_2 L_2

Which implies a similar combination law for \Delta . Using the relationship between the expected CL_s and the luminosity this reduces to

\frac{\Delta}{e^2} = \frac{\Delta_1}{e_1^2} + \frac{\Delta_2}{e_2^2}

This allows us to combine the observed and expected CL_s without knowing the background cross-sections.

Here is what it does for the combination of CDF and Dzero. This is slightly better than my previous attempt when compared with the official combination shown at EPS.

Next here is the new result for the LHC combination that has not yet been shown officially.

As you can see this gives much more significant excesses than my earlier combination. It is even a little above the upper limit of the grey uncertainty area I drew before. The broad excess around 140 GeV is well over three sigma so it can be claimed as an “observation” of a candidate Higgs if this is how the official plot looks. The excess at 120 GeV is also hard to ignore at over 2 sigma and even the limit at the high end near 600 GeV cannot be ruled out. I hope that CERN will decide to extend the plot to higher masses so that we can see this a little better if it appears on their plot.

To look at this in another way we can plot just the size of the excess as seen on the logarithmic graph. In doing so it would be useful to know the expected size of the excess when there is a Higgs boson rather than when there is not as shown on the plot above. I can approximate this by adding 1 to the expected CL_s and showing it with the excess. I also hope CERN will decide to do an accurate version of this or something like it. It is fine to show expected values for no Higgs boson when you are just excluding, but as soon as a signal appears you need to know what a signal is expected to look like with the boson.

This plot is less familiar so let me explain what it is telling us. The black line shows the observed excess in numbers of sigma. There is a broad region of excess above two sigma for masses from 112 GeV to 172 GeV, but this is below the red exclusion line above 149 GeV. It lies within the bands for an expected Higgs boson signal between 110 GeV and 144 GeV. 144 GeV is also where we see the maximum excess at 3.4 sigma, but there is also a minor peak at 119 GeV where the signal reaches 2.6 sigma. Finally there is also a less significant peak at 580 GeV of 1.7 sigma. Although the plot does not exclude a signal for a small window around 250 GeV this is lower than the excess expected for a Higgs boson.

That is not the end of the story because we also have the full Tevatron combination and we can add that in as well to produce a global Higgs combination plot. Nothing changes above 200 GeV so here is a closeup of the  low mass window

The excess at 120 GeV is a little reduced, but otherwise the message is similar.

With twice as much data now recorded by ATLAS and CMS we can expect some clarification on what this is telling us quite soon. Until then the conclusions are uncertain and you are free to speculate.

Higgs Hunting 2011

July 31, 2011

After the hectic EPS conference last week there are a number of followup workshops organised for people to discuss the new results concerning the Higgs boson and possible new physics. The first is the three day meeting “Higgs Hunting 2011″ in Orsay which ended yesterday. For such a workshop the words of the presenters and discussions after are what count, but these are not webcast so all we have to go on as outsiders are the slides (Update 5-Aug-2011: video recordings of the talks have now also been made available at the same link). Nevertheless there are some interesting points in the slides and it is worth picking out some highlights. The workshop started with a talk by Massimiliano Grazzini with this slide showing the main new Higgs results and how it makes the theorists feel These exclusion plots only tell part of the story and it is easy to be misled by excesses that look convincing because they have lots of substructure that makes them appear to show complex signals. In truth the excess comes from a small number of events often seen in just one channel, with the detailed noise coming from the background. A slide from James Olsen for CMS shows the event data from the diphoton channel. On the lefthand plot you can see some excesses at 120 GeV and 140 GeV that make bumps in the exclusion plots but on their own they don’t count for very much. If you look at enough plots you are bound to see excesses of this size somewhere. A slide shown by Elisabetta Pianori shows some signals at around 120 GeV in the same diphoton channels. These are still weak and they are not seen elsewhere. It’s easy to get carried away if you are selective about what you show Here is an more extreme example from Aurelio Juste (see also Paul Thompson). This slide shows events recorded by ATLAS in the H-> ZZ->4l channels. As you can see there are not a lot of events there. This leads to the exclusion limits on the right. As you can see there are bumps giving nearly two sigma excesses, but they correspond to single events. These are not signals on their own. When we combine all the channels and all the experiments we do get some slightly better signals, but still the signal is quite weak. Ben Kilminster has conveniently lined up the plots to show us where they agree, Draw your own conclusions. Here is the update from Matthias Schott on behalf of the gfitter group As you can see they wont include the ATLAS and CMS data anymore claiming that it is “not trivial anymore”. This did not stop John Ellis using the “bloggers combination” to draw some tentative conclusions about the standard model Higgs

The discussion was not just about Higgs but I just have the energy to show one slide summarising the mass limits on various possible new particles according to Paris Sphicas on behalf of ATLAS


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